空间调制傅里叶变换光谱仪分束器色散特性研究

在基于多级微反射镜的傅里叶变换光谱仪中,由于分束器的色散特性, 不同波长的干涉图具有不同的横向偏移量,其在横向空间会发生混叠. 同时,不同波长的干涉图还具有不同的光程差偏移量,使其在纵向空间也会发生混叠. 根据几何光学原理,干涉图的横向混叠会减小干涉图元的有效面积. 计算表明,本研究中干涉图元的横向混叠面积为总面积的3.4%, 通过数据处理扣除混叠部分可以消除横向混叠的影响. 干涉图的纵向混叠会产生一个附加的相位延迟,削弱谱线的强度. 经分析,附加相位延迟与分束器和补偿板之间的厚度差成正比. 本文给出了发生对比度反转时分束器与补偿板厚度差的极限值, 并利用解线性方程组的方法对纵向混叠的干涉图进行了校正, 反演出的光谱与理想光谱的标准偏差仅为1.76×10^-14.

Study on chromatic dispersion of beam splitter in spatially modulated Fourier transform spectrometer

Due to the chromatic dispersion of beam splitter, the interferogram units from various wavelengths could shift by different offsets, leading to interferogram aliasing in transverse space. Simultaneously, the interferograms of different wavelengths have different offsets of optical path difference, which makes the interferogram aliasing in vertical space. According to geometric optics principles, the transverse aliasing of the interferogram reduces the area of the interferogram unit, and the vertical aliasing of the interferogram leads to a phase-frequency response which could reduce the spectral line intensity. The calculation and the analysis indicate that the transverse aliasing area is only 3.4% of the total area of the interferogram unit in our study, which could be removed in the data processing; and the phase delay from the vertical aliasing of the interferogram is proportional to the thickness difference between the beam splitter and the compensating plate. The maximal thickness difference is provided when the contrast reversion appears in the interference fringe. Finally, we correct the chromatic dispersion from the aliasing interferogram by solving linear equation set, and recover the ideal spectrum.